1. Field of the Invention
The present invention is directed to a method for the reconstruction of images with respect to an image plane from measured values acquired with a CT apparatus provided with a detector having at least one line, but preferably a number of lines, of detector elements by conducting a spiral scan, the measured values being respectively allocated to one of a number of projection angles .alpha. and to a z-position on the longitudinal axis of the spiral scan. The invention is also directed to a CT apparatus for the implementation of such a method.
2. Description of the Prior Art
In the reconstruction of images from measured values acquired by spiral scanning with CT apparatus having a single-line detector, an interpolation between the measured values lying in front of and behind the image plane is implemented for each projection angle for generating calculated projections in the desired image plane.
Two interpolation methods are currently most standard:
In the first, a linear interpolation is undertaken between respectively two measured projections lying closest to the image plane, these having been registered at the same projection angle .alpha. but in different revolutions. This type of interpolation is known as 360LI interpolation. In the second method, interpolation is carried out between respectively two projections lying closest to the image plane, of which one projection was registered at the projection angle ad and the other was registered at the projection angle .alpha..sub.c complementary thereto. .alpha..sub.c =.alpha..sub.d.+-..pi. is valid for the middle detector element of the detector. This type of interpolation is known as 180LI interpolation. Given the same pitch, it supplies narrower effective layer widths (characterized, for example, by the full width at half maximum FWHM of the layer sensitivity profile) than the 360LI interpolation. Given the same output power of the x-ray tube (mA value), the pixel noise is increased in comparison to the 360LI interpolation as a trade off. The artifact susceptibility is also higher. Both interpolation types are illustrated schematically in FIG. 2 for the pitch p=2, FIG. 2 showing the projection angle .alpha. as a function of the detector position in the z-direction, with the projection angle .alpha. entered on the longitudinal axis of the spiral scan (z-position) over the position normalized to the width b of a line of the detector. The pitch p is defined as the ratio of the shift in the z-direction per revolution (between the x-ray source/detector and the subject) in mm and the width (in the z-direction) of a line of the detector in mm.
Reconstruction of images from measured values acquired by spiral scan with exact and approximative methods is known for a CT apparatus with multi-line detectors (for example, German PS 196 14 223). These known methods take the exact geometry into consideration but are in part extremely calculation-intensive and therefore poorly suited for use in a commercial CT apparatus.
For reducing the calculating outlay given a low number M of lines (for example, M.ltoreq.5) of the detector, the angle of inclination of the scan rays relative to a plane proceeding perpendicularly to the longitudinal axis of the spiral scan (referred to as the z-axis), known as the cone angle, can be left out of consideration, and the standard 360LI and 180LI interpolation for an apparatus with a single-line detector can be transferred to a number of detector lines. This is the reconstruction technique in the commercial CT apparatus "Elscint Twin" that has a two-line detector (see "Dual-slice versus single-slice spiral scanning: Comparison of the physical performances of two computed tomography scanners", Yun Liang and Robert A. Kruger, Med. Phys. 23(2), February 1996, pp. 205-220). The principle of the 180LI and 360LI interpolation transferred to a number of lines is illustrated in FIG. 3 with reference to the arbitrarily selected example of a 4-line scanner at pitch 3.
The weightings to be taken into consideration in the interpolation are calculated "on the fly" for the interpolation function that has been selected (for example, a triangular function for linear interpolation), this being defined in the apparatus and being capable of being changed only with great difficulty. Given a detector with several lines, the method rapidly encounters practical limits because of the completely modified, relative position of the scan rays on the z-axis for each pitch p.
In the conventional 180LI and 360LI interpolation for a multi-line detector, the slice sensitivity profile for every pitch value p and the pixel noise arising at a fixed output power of the X-ray tube are permanently predetermined by the position of the scan rays on the z-axis. The pixel noise exhibits an unexpected and very sensitive dependency on the pitch p. For example, the scan rays of all four detector lines for a 4-line detector given the pitch p=1 are incident on the same z-positions in successive revolutions. Therefore they can simply be averaged before the interpolation, and a dose accumulation by the factor 4, and thus a halving of the pixel noise by comparison to the one-liner with 360LI interpolation, occurs as a result. When the pitch p is increased only slightly, for example to p=1.1, this multiple scanning is eliminated. A narrower slice sensitivity profile is obtained in the 180LI and 360LI interpolation, but at the expense of the same pixel noise as for a one-line detector. According to the known method, it is not possible, given small pitch values (for example, p=1.1, as above), to utilize the overlapping scanning in the z-direction for the purpose of reducing the pixel noise while simultaneously broadening the slice sensitivity profile.
Given the known methods provided for employment with multi-line detector, moreover, the measured values of all lines of the detector are weighted for each projection angle only according to their distance from the image plane, without considering the time at which the measured values were acquired. As a result, an enlargement of the time window during which measured values are acquired that contribute to an image derives as the pitch becomes smaller. For a 4-line detector and a pitch p=1, for example, not only is the aforementioned quadrupling of the dose in the image obtained compared to a one-line CT apparatus, but also a lengthening of the image-relevant window occurs to four times the duration of a complete revolution of the X-ray source. Particularly in exposures of moving subjects such as, for example, high-resolution lung exposures, this can lead to a noticeable limitation of the image quality.